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Nominal rewriting systems

Maribel Fernández, Murdoch J. Gabbay, Ian Mackie
2004 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '04  
as nominal rewriting systems.  ...  This shows that nominal rewriting is as expressive as standard higher-order rewriting systems.  ...  Nominal rewriting is also related to Hamana's Binding Term Rewriting Systems (BTRS) [17] .  ... 
doi:10.1145/1013963.1013978 dblp:conf/ppdp/FernandezGM04 fatcat:rf2jbm6b4nhkhfc4nzz7vw72cq

Nominal Completion for Rewrite Systems with Binders [chapter]

Maribel Fernández, Albert Rubio
2012 Lecture Notes in Computer Science  
Her expertise is in type systems, semantics, and foundations of security, using rewrite-based techniques (term and graph rewriting, and lambda-calculus).  ...  Maribel Fernández, King's College London Facultad de Informática Aula 14  5 de julio de 2012  12:00 entrada libre hasta completar el aforo resumen: Nominal rewriting generalises first-order rewriting  ... 
doi:10.1007/978-3-642-31585-5_21 fatcat:t7wwtpb5lneipghk4qv7pnfq64

Parallel Closure Theorem for Left-Linear Nominal Rewriting Systems [chapter]

Kentaro Kikuchi, Takahito Aoto, Yoshihito Toyama
2017 Lecture Notes in Computer Science  
The results include confluence of left-linear uniform nominal rewriting systems that are not α-stable and thus are not represented by any systems in traditional higher-order rewriting frameworks.  ...  In this paper, we extend Huet's parallel closure theorem and its generalisation on confluence of left-linear term rewriting systems to the case of nominal rewriting.  ...  rewriting systems Nominal rewrite rules and nominal rewriting systems are defined as follows.  ... 
doi:10.1007/978-3-319-66167-4_7 fatcat:72fqmusg4bfhzfjsl4zdwye7zq

Closed nominal rewriting and efficiently computable nominal algebra equality

Maribel Fernández, Murdoch J. Gabbay
2010 Electronic Proceedings in Theoretical Computer Science  
We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories.  ...  With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality.  ...  However, nominal rewrite/algebra systems exist that do not fall into the closed collection.  ... 
doi:10.4204/eptcs.34.5 fatcat:bicszfopmzantfxuzzbt64ty2e

Principal Types for Nominal Theories [chapter]

Elliot Fairweather, Maribel Fernández, Murdoch J. Gabbay
2011 Lecture Notes in Computer Science  
We define rank 1 polymorphic types for nominal rewrite rules and equations.  ...  Our system has principal types, and we give rule and axiom formats to guarantee preservation of types under both rewriting and equality reasoning.  ...  In Section 2 we recall nominal rewriting and equational reasoning, as well as the Curry-style type system for nominal terms.  ... 
doi:10.1007/978-3-642-22953-4_14 fatcat:cn2nju2fcbgehjrajc355xatmm

Typed Nominal Rewriting

Elliot Fairweather, Maribel Fernández
2018 ACM Transactions on Computational Logic  
However, thus far, formal research in type systems for nominal abstract syntax, nominal terms and nominal rewriting has been limited (see Related Work below).  ...  This system is then used to define two presentations of typed nominal rewriting, one more expressive and one more efficient, the latter also giving rise to a notion of typed nominal equational reasoning  ...  Thus a system of typed closed nominal rewriting is highly desirable.  ... 
doi:10.1145/3161558 fatcat:ghyr5ru2sjhi3ib4wdtsny23uq

Nominal rewriting with name generation

Maribel Fernández, Murdoch J. Gabbay
2005 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '05  
Finally, we study confluence properties of nominal rewriting and its extensions.  ...  Nominal rewriting extends first-order rewriting with Gabbay-Pitts abstractors: bound entities are explicitly named (rather than being nameless, as for de Bruijn indices) yet rewriting respects α-conversion  ...  Nominal rewriting is also related to Hamana's Binding Term Rewriting Systems (BTRS) [19] .  ... 
doi:10.1145/1069774.1069779 dblp:conf/ppdp/FernandezG05 fatcat:kz7q6u6szvd6xdd5tdiilp6a5a

Nominal rewriting

Maribel Fernández, Murdoch J. Gabbay
2007 Information and Computation  
Nominal rewriting is based on the observation that if we add support for -equivalence to first-order syntax using the nominal-set approach, then systems with binding, including higher-order reduction schemes  ...  We show how good properties of first-order rewriting survive the extension, by giving an efficient rewriting algorithm, a critical pair lemma, and a confluence theorem for orthogonal systems.  ...  We can formally define ca using a nominal rewriting system, where we add two new kinds of constraints: •t (read t is closed), with the intended meaning "a#t for every atom a", and a ∈ t (read a is unabstracted  ... 
doi:10.1016/j.ic.2006.12.002 fatcat:myd23ts6s5ernh6gx6gwouy5yu

Hierarchical Nominal Terms and Their Theory of Rewriting

Murdoch J. Gabbay
2007 Electronical Notes in Theoretical Computer Science  
Nominal rewriting introduced a novel method of specifying rewriting on syntax-with-binding.  ...  To the extent that rewriting is a mathematical metaframework for logic and computation, and nominal rewriting is a framework with native support for binders, hierarchical nominal term rewriting is a meta-to-the-omega  ...  Call a possibly infinite set of hierarchical nominal rewrite rules a hierarchical nominal (term) rewrite system.  ... 
doi:10.1016/j.entcs.2007.01.017 fatcat:qbexpjcdsrbtlkybject2t375a

Introduction to the special issue: Unification

Mauricio Ayala-Rincón, Philippe Balbiani
2020 Mathematical Structures in Computer Science  
With the advent of automated reasoning, term rewriting, logic programming, natural language processing, and program analysis, the areas of computer science concerned by unification were seething with excitement  ...  The most elaborated aspect is the adaptation of a Knuth-Bendix confluence criterion for such nominal systems.  ...  The first solves the deduction and static equivalence problems in rewrite systems modulo shallow theories.  ... 
doi:10.1017/s0960129520000237 fatcat:l3ny2xfhq5grvl34lremb7z6hi

Nominal Narrowing

Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho, Marc Herbstritt
2016 International Conference on Rewriting Techniques and Applications  
Nominal unification is a generalisation of first-order unification that takes α-equivalence into account. In this paper, we study nominal unification in the context of equational theories.  ...  We introduce nominal narrowing and design a general nominal E-unification procedure, which is sound and complete for a wide class of equational theories. We give examples of application.  ...  defined by convergent closed nominal rewriting systems.  ... 
doi:10.4230/lipics.fscd.2016.11 dblp:conf/rta/Ayala-RinconFN16 fatcat:fviazu4ugreubewkquygld3f64

Checking Overlaps of Nominal Rewriting Rules

Mauricio Ayala-Rincón, Maribel Fernández, Murdoch James Gabbay, Ana Cristina Rocha-Oliveira
2016 Electronical Notes in Theoretical Computer Science  
Nominal rewriting generalises first-order rewriting by providing support for the specification of binding operators.  ...  More precisely, we show that closed nominal rewriting rules where all proper critical pairs are joinable are locally confluent.  ...  We intend to enlarge the PVS library on term rewriting systems [10] to formalise the results of this paper.  ... 
doi:10.1016/j.entcs.2016.06.004 fatcat:3khq65svebalndqv6pfp2ihhfu

Equivariant Unification

James Cheney
2009 Journal of automated reasoning  
It serves as the basis of logic programming and term rewriting techniques that provide similar advantages to, but remain simpler than, higher-order logic programming or term rewriting systems.  ...  Previous work on nominal rewriting and logic programming has relied on nominal unification, that is, unification up to equality in nominal logic.  ...  This algorithm can be used to run arbitrary nominal logic programs and rewriting systems and may also be useful in analyzing such systems.  ... 
doi:10.1007/s10817-009-9164-3 fatcat:rocbgzpyszfjrprwqqnjjxb6na

Equivariant Unification [chapter]

James Cheney
2005 Lecture Notes in Computer Science  
It serves as the basis of logic programming and term rewriting techniques that provide similar advantages to, but remain simpler than, higher-order logic programming or term rewriting systems.  ...  Previous work on nominal rewriting and logic programming has relied on nominal unification, that is, unification up to equality in nominal logic.  ...  This algorithm can be used to run arbitrary nominal logic programs and rewriting systems and may also be useful in analyzing such systems.  ... 
doi:10.1007/978-3-540-32033-3_7 fatcat:r3asbtufxvesrjghtyqeclp4ui

Implementing Nominal Unification

Christophe Calvès, Maribel Fernández
2007 Electronical Notes in Theoretical Computer Science  
Nominal matching and unification underly the dynamics of nominal rewriting.  ...  Urban, Pitts and Gabbay gave a nominal unification algorithm which finds the most general solution to a nominal matching or unification problem, if one exists.  ...  As such, it is well-adapted to implementing algorithms specified as rewriting systems.  ... 
doi:10.1016/j.entcs.2006.09.027 fatcat:oq3nhp3x2ffklifcjjv3nchs34
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